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How many natural numbers are their from 1 to 1000 which have none of their digits repeated.
Correct answer is '738'. Can you explain this answer?
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How many natural numbers are their from 1 to 1000 which have none of t...
Solution:
To find the number of natural numbers from 1 to 1000 which have none of their digits repeated, we can follow the below steps:
Step 1: Count the numbers with a single digit
- There are 9 such numbers (1, 2, 3, 4, 5, 6, 7, 8, 9)
Step 2: Count the numbers with two digits
- The first digit can be any of the 9 digits (excluding 0)
- The second digit can be any of the 9 remaining digits (excluding the first digit)
- So, there are 9 x 9 = 81 such numbers
Step 3: Count the numbers with three digits
- The first digit can be any of the 9 digits (excluding 0)
- The second digit can be any of the 9 remaining digits (excluding the first digit)
- The third digit can be any of the 8 remaining digits (excluding the first two digits)
- So, there are 9 x 9 x 8 = 648 such numbers
Step 4: Add up the numbers from all the steps
- Total number of natural numbers from 1 to 1000 which have none of their digits repeated = 9 + 81 + 648 = 738
Therefore, the correct answer is '738'.
To find the number of natural numbers from 1 to 1000 which have none of their digits repeated, we can follow the below steps:
Step 1: Count the numbers with a single digit
- There are 9 such numbers (1, 2, 3, 4, 5, 6, 7, 8, 9)
Step 2: Count the numbers with two digits
- The first digit can be any of the 9 digits (excluding 0)
- The second digit can be any of the 9 remaining digits (excluding the first digit)
- So, there are 9 x 9 = 81 such numbers
Step 3: Count the numbers with three digits
- The first digit can be any of the 9 digits (excluding 0)
- The second digit can be any of the 9 remaining digits (excluding the first digit)
- The third digit can be any of the 8 remaining digits (excluding the first two digits)
- So, there are 9 x 9 x 8 = 648 such numbers
Step 4: Add up the numbers from all the steps
- Total number of natural numbers from 1 to 1000 which have none of their digits repeated = 9 + 81 + 648 = 738
Therefore, the correct answer is '738'.
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How many natural numbers are their from 1 to 1000 which have none of their digits repeated.Correct answer is '738'. Can you explain this answer?
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How many natural numbers are their from 1 to 1000 which have none of their digits repeated.Correct answer is '738'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about How many natural numbers are their from 1 to 1000 which have none of their digits repeated.Correct answer is '738'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many natural numbers are their from 1 to 1000 which have none of their digits repeated.Correct answer is '738'. Can you explain this answer?.
How many natural numbers are their from 1 to 1000 which have none of their digits repeated.Correct answer is '738'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about How many natural numbers are their from 1 to 1000 which have none of their digits repeated.Correct answer is '738'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many natural numbers are their from 1 to 1000 which have none of their digits repeated.Correct answer is '738'. Can you explain this answer?.
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